Projects per year

### Abstract

This thesis investigates new optimization methods for structural topology optimization
problems. The aim of topology optimization is finding the optimal design of a structure.
The physical problem is modelled as a nonlinear optimization problem. This powerful
tool was initially developed for mechanical problems, but has rapidly extended to many
other disciplines, such as fluid dynamics and biomechanical problems. However, the
novelty and improvements of optimization methods has been very limited. It is, indeed,
necessary to develop of new optimization methods to improve the final designs, and at the
same time, reduce the number of function evaluations. Nonlinear optimization methods,
such as sequential quadratic programming and interior point solvers, have almost not
been embraced by the topology optimization community. Thus, this work is focused on
the introduction of this kind of second-order solvers to drive the field forward.
The first part of the thesis introduces, for the first time, an extensive benchmarking
study of different optimization methods in structural topology optimization. This comparison
uses a large test set of instance problems and three different structural topology
optimization problems.
The thesis additionally investigates, based on the continuation approach, an alternative
formulation of the problem to reduce the chances of ending in local minima, and at
the same time, decrease the number of iterations.
The last part is focused on special purpose methods for the classical minimum compliance
problem. Two of the state-of-the-art optimization algorithms are investigated and
implemented for this structural topology optimization problem. A Sequential Quadratic
Programming (TopSQP) and an interior point method (TopIP) are developed exploiting
the specific mathematical structure of the problem. In both solvers, information of the
exact Hessian is considered. A robust iterative method is implemented to efficiently solve
large-scale linear systems. Both TopSQP and TopIP have successful results in terms of
convergence, number of iterations, and objective function values. Thanks to the use of
the iterative method implemented, TopIP is able to solve large-scale problems with more
than three millions degrees of freedom.

Original language | English |
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Publisher | DTU Wind Energy |
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Number of pages | 239 |

Publication status | Published - 2015 |

## Projects

- 1 Finished

## Mathematical Programming in Topology and Large Scale Optimization of Structures

Duysinx, P. & Bendsøe, M. P.

01/09/1996 → 31/08/1997

Project: Research

## Cite this

Rojas Labanda, S. (2015).

*Mathematical programming methods for large-scale topology optimization problems*. DTU Wind Energy.